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We investigate the transient dynamics of a sheared suspension of neutrallybuoyant particles under pressure-imposed conditions, subject to a sudden changein shear rate or external pressure. Discrete Element Method simulations showthat, depending on the flow parameters (particle and system size, initialvolume fraction), the early stress response of the suspension may stronglydiffer from the prediction of the Suspension Balance Model based on thesteady-state rheology. We show that a two-phase model incorporating theReynolds-like dilatancy law of Pailha & Pouliquen (2009), which prescribes thedilation rate of the suspension over a strain scale $\gamma_0$, quantitativelycaptures the suspension dilation/compaction over the whole range of parametersinvestigated. Together with the Darcy flow induced by the pore pressuregradient during dilation or compaction, this Reynolds-like dilatancy impliesthat the early stress response of the suspension is nonlocal, with a nonlocallength scale $\ell$ which scales with the particle size and divergesalgebraically at jamming. In regions affected by $\ell$, the stress level isfixed, not by the steady-state rheology, but by the Darcy fluid pressuregradient resulting from the dilation/compaction rate. Our results extend thevalidity of the Reynolds-like dilatancy flow rule, initially proposed forjammed suspensions, to flowing suspension below $\phi_\mathrm{c}$, therebyproviding a unified framework to describe dilation and shear-induced migration.They pave the way for understanding more complex unsteady flows of densesuspensions, such as impacts, transient avalanches or the impulsive response ofshear-thickening suspensions.

Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy